Re: More complex numbers than reals?

Am 11.07.2024 um 02:33 schrieb Chris M. Thomasson:

On 7/10/2024 5:31 PM, Moebius wrote:

Am 11.07.2024 um 02:28 schrieb Chris M. Thomasson:

On 7/10/2024 5:24 PM, Moebius wrote:

Am 11.07.2024 um 02:16 schrieb Chris M. Thomasson:
>

{a, b, c} vs { 3, 4, 5 }
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Both have the same number of elements, [...]

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HOW do you know that? Please define (for any sets A, B):
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     A and B /have the same number of elements/ iff _______________ .
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(i.e. fill out the blanks). :-)
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Hint: That's what Ben Bacarisse is asking for.
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Sure, it's "obvious" for us.

Actually, it's not, since we don't know if a, b, c are "pairwise distinct" (see below). Sorry about that.

But how would you define "have the same  number of elements" (in mathematical terms) such that it can be  DEDUCED (!) für certain sets A and B?

Yes?

________________________________________
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Ok, I'm slighty wicked now... :-)
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If a = b = c, {a, b, c} still has "the same number of elements" as {3, 4, 5 }? :-P

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I see {a, b, c} and {3, 4, 5} and think three elements.

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Even if a = b = c?
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C'mon man! :-P

 Well, In my programming mind, { a, b, c } and { 3, 4, 5 } have the same number of elements. Is this bad?

Yes it's bad. :-)
If a = b = c, then {a, b, c} only contains 1 element.
Don't mix up the symbols used for denoting some objects with the objects denoted by the symbols.
In this case there are 3 (different) symbols, namely "a", "b", "c", but it is not excluded that they all denote the same object, say, the number 1. Then {a, b, c} = {1}.
I hope "In my programming mind" knows the difference beween using
       a, b, b
and
       "a", "b", "c".
:-)
Hint (Python):
a = 1
print(a)
print("a")
:-P